When I was learning guitar in the 60s that's usually what it was called, "the Blue Moon sequence". You know - C, Am, F, G, with variations, like Dm instead of F. This one - "Moths", by Jethro Tull - contains more complex harmonies too, but it uses that sequence as the core of the melody, and it's possibly the most perfect example of what you can do with a very simple (even clichéd) chord progression. I think it's quite sublime.

BTW - Did you guys remember Del Shannon was the 1st to get airplay in the US with a Lennon-McCartney tune? He did "From Me to You" very soon after it was released, and it was played on a midwest radio station. Apparently he did the England tour with the other Yanks in '62 or '63, heard them do it live, and came right back home and recorded it. There's an old thread around somewhere about that with a music clip, but since it's not Blue Moon chords, I won't hijack this thread (any more - sorry!).

Funny thing is ... on Elvis' Sun Sessions Blue Moon recording, it sure is hard to hear the Blue Moon progression! He kind of rocks it up ...